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Plug-in L2-upper error bounds in deconvolution, for a mixing density estimate in Rd and for its derivatives, via the L1-error for the mixture
Statistics ( IF 1.2 ) Pub Date : 2019-07-30 , DOI: 10.1080/02331888.2019.1632313
Yannis G. Yatracos 1, 2
Affiliation  

ABSTRACT In deconvolution in with mixing density and kernel h, the mixture density is estimated with MDE having upper -error rate, in probability or in risk; . In one application, consists of -separable densities in R with differences changing sign at most J times and Totally Positive. When h is known and p is -smooth, vanishing outside a compact in plug-in upper bounds are provided for the -error rate of and its -th mixed partial derivative via , with rates and , respectively, for h super-smooth and smooth; . For the former rate is optimal for any and the latter misses the optimal by the factor when . and appear in optimal rates and lower error and risk bounds in the deconvolution literature.

中文翻译:

去卷积中的插件 L2 误差上限,用于 Rd 中的混合密度估计及其导数,通过混合物的 L1 误差

摘要 在混合密度和核 h 的反卷积中,混合密度用具有较高错误率、概率或风险的 MDE 估计;. 在一个应用程序中,由 R 中的可分离密度组成,差异最多改变符号 J 次且完全为正。当 h 已知且 p 为 -smooth 时,为 h 的 -error rate 及其第 -th 混合偏导数提供了消失在插件上限的紧凑外,分别具有 rate 和 ,对于 h 超平滑和平滑; . 因为前者的速率对于任何一个都是最优的,而后者在 时因因子而错过了最优值。并且在解卷积文献中以最优速率和较低的错误和风险界限出现。
更新日期:2019-07-30
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